The research in industry and academia on smart grids is predominantly focused on the regulation of generated power and management of its consumption. Because transmission of bulk-generated power to the consumer is immensely reliant on secure and efficient transmission grids, comprising huge electrical and mechanical assets spanning a vast geographic area, there is an impending need to focus on the transmission grids as well. Despite the challenges in wireless technologies for SGs, cognitive radio networks are considered promising for provisioning of communications services to SGs. In this paper, first, we present an IEEE 802.22 wireless regional area network cognitive radio-based network model for smart monitoring of transmission lines. Then, for a prolonged lifetime of battery finite monitoring network, we formulate the spectrum resource allocation problem as an energy efficiency maximization problem, which is a nonlinear integer programming problem. To solve this problem in an easier way, we propose an energy-efficient resource-assignment scheme based on the Hungarian method. Performance analysis shows that, compared to a pure opportunistic assignment scheme with a throughput maximization objective and compared to a random scheme, the proposed scheme results in an enhanced lifetime while consuming less battery energy without compromising throughput performance.